Search

This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion (S p VI s P) and its extended version for estimating the common solution of (S p VI s P) and fixed point problem (FPP) of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we alter Wang's new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem ( S p VIP) in Hilbert space. We discuss the weak convergence for ( S p VIP) and strong convergence for the common solution of ( S p VIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes. [ABSTRACT FROM AUTHOR]

In this article, we consider a split monotone variational inclusions constraints over the set of fixed points of finite families of firmly non-expansive mappings, named split hierarchical monotone variational inclusions problem (in short: SHMVIP). We propose an iterative algorithm for solving SHMVIP. Further, we prove that the sequence generated by proposed algorithm converges weakly to the solution of SHMVIP. Strong convergence of the iterative algorithm is also discussed under some suitable assumptions. We give an example in support of our problem. [ABSTRACT FROM AUTHOR]